This paper aims at characterizing the long time evolution of the vehicle-track system. The knowledge of the evolution of such a system is of great concern for the railway industry, in order to maintain a high level of safety and comfort in the high speed trains. We propose a computational stochastic approach to predict the long time evolution of a given track portion. The approach is based on an adaptation of the global stochastic model of track irregularities previously identified with a large experimental data basis. The nonlinear stochastic dynamics of the train excited by track irregularities are carried out using a computational multibody dynamics model. Some indicators concerning the dynamic responses of the train are introduced in order to start off the maintenance or not of the given track portion.